Sum of squares approach for nonlinear \(\operatorname{H}_\infty\) control
type: Item
instance of: scholarly article
title: Sum of squares approach for nonlinear \(\operatorname{H}_\infty\) control
zbMATH Open document ID: 1407.93115
DOI: 10.1155/2018/8325609
author: Ai-ping Pang
author: Zhen He
author: Ming-han Zhao
author: Guangxiong Wang
author: Qin-mu Wu
author: Ze-Tao Li
published in: Complexity
publication date: 2019-02-19T00:00:00Z
review text: Summary: A proper Hamilton-Jacobi-Isaacs (HJI) inequality must be solved in a nonlinear \(\operatorname{H}_\infty\) control problem. The sum of squares (SOS) method can now be used to solve an analytically unsolvable nonlinear problem. A HJI inequality suitable for SOS approach is derived in the paper. The SOS algorithm for solving the HJI inequality is also provided. Conservativeness of the SOS method is then discussed in the paper. The conservativeness of the SOS approach is caused by the method itself, because it is really a synthesis method over the entire state space. To reduce the conservativeness, a local \(\operatorname{H}_\infty\) design on a restricted state-space region is proposed. But the SOS approach for the local \(\operatorname{H}_\infty\) design also suffers from the conservativeness problem, because the S-procedure for solving the set-containment constraint provides only a sufficient condition. The above-mentioned sources of conservativeness are peculiar for the SOS approaches. So a proper approach must be carefully selected in the design process to get a reasonable result. A design example is also given in the paper.
Mathematics Subject Classification ID: 93B36
Mathematics Subject Classification ID: 93C10
zbMATH DE Number: 7025192
describes a project that uses: Sostools
describes a project that uses: SPOTless
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2018/8325609
OpenAlex ID: W2903090916
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description: scientific article; zbMATH DE number 7025192